R A N D O M M A T R I X T H E O R Y, S P R I N G 2 0 1 5
Lectures: Tuesday, 1.25pm-3.15pm, in Warren Weaver Hall 1302.
Lecturer: Paul Bourgade. For office hours, you can set up an appointment or just drop by (Warren Weaver Hall 603).
This course will introduce techniques to understand the spectrum and eigenvectors of large random self-adjoint matrices, on both global and local scales. Topics include Gaussian ensembles, Dyson's Brownian motion, determinantal processes, bulk and edge scaling limits, universality for random matrices.
Prerequisites: Basic knowledge of linear algebra, probability theory and stochastic calculus is required.
Textbooks: There is no reference book for this course. Possible useful texts are:
Greg Anderson, Alice Guionnet and Ofer Zeitouni. An Introduction to Random Matrices.
Percy Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Percy Deift and Dimitri Gioev, Random Matrix Theory: Invariant Ensembles and Universality.
Laszlo Erdos, lecture notes on universality for random matrices and log-gases.
Homework: Once a month.
Grading: Based on problem sets and attendance/participation at lectures.
A tentative schedule for this course is: